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arXiv:2512.19255

Optical parametric free-electron--photon quantum interaction

Zetao Xie, Zehai Pang, Yi Yang

physics.opticscond-mat.mes-hallphysics.acc-phquant-phSubmitted Dec 22, 2025• Announced Dec 23, 2025• 0 citations

Abstract

Optical parametric processes underpin quantum photonics, while free-electron--photon interactions offer agile pathways to generate nontrivial quantum photonic states. These threads have so far largely progressed independently, whereas placing free electrons in a driven nonlinear system can potentially activate coherent parametric interaction channels for joint state engineering of both types of particles. Here we unify these paradigms by developing a general theoretical framework for parametric free-electron--photon interactions in a nonlinear optical system driven by degenerate parametric down-conversion. Unlike free electrons in a linear bath, here they can couple to Bogoliubov quasiparticles through two detuned phase-matching channels, where the parametric process and free-electron interactions can quantum amplify each other. Seeding the interaction with squeezed vacuum yields gain-only or loss-only electron energy spectra, and enables electron-heralded squeezed Fock states; with bare vacuum, postselecting electron energy sidebands generates high-fidelity Schrödinger cat states. Our results show how optical parametric interactions can quantum shape free electrons and photons, potentially enabling a quantum parametric dielectric laser accelerator that mitigates the need for temporal phase synchronization, thereby allowing acceleration probabilities to approach unity even for phase-random electrons.

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Realization of quantum nonlinearity in quadratic optomechanics, including optical and mechanical nonlinearity at the single-photon level, is crucial to explore extraordinary quantum features. Here we investigate an exponential enhancement of quadratic optomechanical interaction via parametric amplifications. The parametric process can form an in-phase amplified quadrature, and the rate of coupling to the in-phase quadrature will be exponentially increased even to the single-photon strong-coupling regime. Concretely, to achieve the optical nonlinearity mediated by the quadratic optomechanical interaction, we can employ a mechanical parametric process, and the in-phase mechanical quadrature can strongly couple to the cavity mode, leading to an enhanced optical nonlinearity such as a photon blockade. Similarly, via employing the optical parametric process, the in-phase optical quadrature can also effectively mediate the quadratic interaction, leading to an enhanced mechanical nonlinearity such as mechanical squeezing, bi-excitation exchange interaction and feasibility of quantum non-demolition detection of mechanical motion. However, the parametric process can also enlarge the noise, and a squeezing vacuum with the phase matching condition should be introduced to suppress the same.